The core counts on all the challenger divisions apply to the native core count.
I have used a 7980xe in the Pro OC and Div I stages.
Div II needs a 9900K, 7820X or 9800X, which are inherently 8-core processors.
A 7800X would work in the 6-core Div III, but I'll be using a 8700K.
The quad core Div IV needs a 7740X, 7700K or 6700K.
Haswell and older 4-core CPUs would place better in the 'legacy' Div VII.